Surveillance cameras typically are stationary or have controllable motions, such as pan, tilt, and zoom. Therefore, the background scene can be considered stationary. Conventionally, surveillance videos are obtained by acquiring each pixel value (raster scan) of the scene with a stationary background over a long period of time. Such surveillance cameras create a massive amount of data and consume a lot of power. Since the background is stationary, power consumption can be reduced if only the moving foreground is measured. However, this is challenging because the location of the moving foreground can be arbitrary and usually unknown until the entire scene is acquired.
There are a few related works that detect foreground from a stationary background video. For example, the authors in Candes et al. show that the low-rank and sparse components of a matrix can be separated exactly by convex programming (see E. Candes, X. Li, Y. Ma, and J. Wright, “Robust Principal Component Analysis?”, IEEE PAMI 2011). They demonstrate this in a video surveillance application in which they stack video frames as columns of a matrix, which can be decomposed into a low-rank component that represents the stationary background and a sparse component that represents moving objects. The process proposed by Candes et al. is entirely post-processing.
In Peng et al., Candes et al.'s work was extended by simultaneously aligning a batch of images that are linearly correlated and with corruption such as occlusion (see Y. Peng, A. Ganesh, J. Wright, W. Xu, and Y. Ma, “RASL: Robust Alignment by Sparse and Low-rank Decomposition for Linearly Correlated Images”, IEEE PAMI 2011). Each column of the matrix, which is an image, finds an optimal transform so that the matrix can be decomposed into a low-rank component and a sparse component. This is also post processing and does not involve video acquisition.
Two groups have investigated the problem of low-rank and sparse recovery from compressive measurements. For example, Waters et al. introduced an effective alternating minimization algorithm for compressive low-rank and sparse recovery (see A. Waters, A. Sankaranarayanan, and R. Baraniuk. SparCS: Recovering low-rank and sparse matrices from compressive measurements. NIPS, 2011). Additionally, Wright et al. developed theoretical conditions under which compressive low-rank and sparse recovery can be solved with a convex optimization (see J. Wright, A. Ganesh, K. Min, and Y. Ma. Compressive Principal Component Pursuit, ISIT, 2012). However, these background modeling methods for compressive low-rank and sparse recovery can only process multiple video frames in batch fashion, limiting their application to real time video surveillance and are not designed to reduce the power consumption of the imaging system.
Thus, a continuing need exists for an efficient surveillance system that detects interesting targets and intruders without acquiring massive surveillance video data.